Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26041241 | C2 | semidirect |
| 3. #26041138 | C2 | semidirect |
| 4. #26041016 | C2 | semidirect |
| 5. #26041014 | C2 | semidirect |
| 6. #26041012 | C2 | semidirect |
| 7. #328×C181 | C2 | semidirect |
| 8. C2×#15668450 | C4 | semidirect |
| 12. #19153792 | C4 | semidirect |
| 13. #19153791 | C4 | semidirect |
| 18. #19153774 | C4 | semidirect |
| 128. C181 | #1513 | semidirect |
| 134. #328 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041792 | 2 |
| #26041241 | 2 |
| #26041138 | 2 |
| #26041016 | 2 |
| #26041014 | 2 |
| #26041012 | 2 |
| #328×C181 | 2 |
| #1513 | 181 |